Archive for February, 2016

What is the size of a molecule that will stretch computational resources today? Chan and co-workers have examined some very large fullerenes1 to both answer that question, and also to explore how large a fullerene must be to approach graphene-like properties.

They are interested in predicting the heat of formation of large fullerenes. So, they benchmark the heats of formation of C60 using four different isodesmic reactions (Reaction 1-4), comparing the energies obtained using a variety of different methods and basis sets to those obtained at W1h. The methods include traditional functionals like B3LYP, B3PW91, CAM-B3LYP, PBE1PBE, TPSSh, B98, ωB97X, M06-2X3, and MN12-SX, and supplement them with the D3 dispersion correction. Additionally a number of doubly hybrid methods are tested (again with and without dispersion corrections), such as B2-PLYP, B2GPPLYP, B2K-PLYP, PWP-B95, DSD-PBEPBE, and DSD-B-P86. The cc-pVTZ and cc-pVQZ basis sets were used. Geometries were optimized at B3LYP/6-31G(2df,p).

C60 + 10 benzene → 6 corannulene

Reaction 1

C60 + 10 naphthalene → 8 corannulene

Reaction 2

C60 + 10 phenanthrene → 10 corannulene

Reaction 3

C60 + 10 triphenylene → 12 corannulene

Reaction 4

Excellent results were obtained with DSD-PBEPBE-D3/cc-pVQZ (an error of only 1.8 kJ/mol), though even a method like BMK-D3/cc-pVTZ had an error of only 9.2 kJ/mol. They next set out to examine large fullerenes, including such behemoths as C180, C240, and C320, whose geometries are shown in Figure 1. Heats of formation were obtained using isodesmic reactions that compare back to smaller fullerenes, such as in Reaction 5-8.

C70 + 5 styrene → C60 + 5 naphthalene

Reaction 5

C180 → 3 C60

Reaction 6

C320 + 2/3 C60 → 2 C180

Reaction 7

C180

C240

C320

Figure 1. B3LYP/6-31G(2df,p) optimized geometries of C180, C240, and C320. (Don’t forget that clicking on these images will launch Jmol and allow you to manipulate the molecules in real-time.)

Next, taking the heat of formation per C for these fullerenes, using a power law relationship, they were able to extrapolate out the heat of formation per C for truly huge fullerenes, and find the truly massive fullerenes, like C9680, still have heats of formation per carbon 1 kJ/mol greater than for graphene itself.

Atropisomers are stereoisomer that differ by axial symmetry, such as in substituted biphenyls or allenes. These acyclic systems have received a fair amount of attention, but now Buevich has looked at atropisomerization that occurs in a ring system.11 has a biphenyl as part of the eight-member ring, and the biphenyl can exist in either an M or P orientation. Since C3 is chiral (S), the two isomers are (M,S)-1 and (P,S)-1. Variable temperature NMR analysis concludes that (P,S)-1 is 1.19 kcal mol-1 more stable than (M,S)-1, and the barrier for the interchange (P,S)-1 → (M,S)-1 is 26.77 kcal mol-1.

To identify the process for this atropisomerization process, he utilized B3LYP/6-31G(d) computations of the model system 2. A variety of different techniques were used to identify the local energy minimum conformations of both (M,S)-2 and (P,S)-2, and the lowest energy conformers (M1 for (P,S)-2 and M4 for (M,S)-2) are shown in Figure 1. He then produced a series of 2-D potential energy surfaces varying two of the dihedral angles defining the eight-member ring to help identify potential initial geometries for searching for transition states. (As an aside, this procedure ended up identifying a few additional local energy minima not identified in the initial conformational search – and these all have trans amide groups instead of the cis relationship found initially. These trans isomer are considerably higher in energy than the conformers.) With this model and this computational level, (P,S)-2 is 0.76 kcal mol-1 lower in energy than (M,S)-2.

A number of transition states were identified, and the lowest energy pathway that takes M1 into M4 first crosses TS1 to make the minimum M2, which than passes a high barrier (25.8 kcal mol-1) to go to M4. This barrier is in reasonable agreement with the experimental barrier for 1. These TSs are also shown in Figure 1.

Buevich analyzes the conformational process by examination of the changes in the ring dihedral angles following this reaction path. As expected, crossing the highest barrier requires a combination of torsional rotations, but essentially one at a time moving clockwise about the ring.

I discuss the aqueous Diels-Alder reaction in Chapter 7.1 of my book. A key case is the reaction of methyl vinyl ketone with cyclopentadiene, Reaction 1. The reaction is accelerated by a factor of 740 in water over the rate in isooctane.1 Jorgensen argues that this acceleration is due to stronger hydrogen bonding to the ketone than in the transition state than in the reactants.2-4

Rxn 1

Doubleday and Houk5 report a procedure for calculating trajectories including explicit water as the solvent and apply it to Reaction 1. Their process is as follows:

Compute the endo TS at M06-2X/6-31G(d) with a continuum solvent.

Equilibrate water for 200ps, defined by the TIP3P model, in a periodic box, with the transition state frozen.

Continue the equilibration as in Step 2, and save the coordinates of the water molecules after every addition 5 ps, for a total of typically 25 steps.

For each of these solvent configurations, perform an ONIOM computation, keeping the waters fixed and finding a new optimum TS. Call these solvent-perturbed transition states (SPTS).

Generate about 10 initial conditions using quasiclassical TS mode sampling for each SPTS.

Now for each the initial conditions for each of these SPTSs, run the trajectories in the forward and backward directions, typically about 10 of them, using ONIOM to compute energies and gradients.

A few SPTS are also selected and water molecules that are either directly hydrogen bonded to the ketone, or one neighbor away are also included in the QM portion of the ONIOM, and trajectories computed for these select sets.

The trajectory computations confirm the role of hydrogen bonding in stabilizing the TS preferentially over the reactants. Additionally, the trajectories show an increasing asynchronous reactions as the number of explicit water molecules are included in the QM part of the calculation. Despite an increasing time gap between the formation of the first and second C-C bonds, the overwhelming majority of the trajectories indicate a concerted reaction.